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Video: Converting an Equation from Exponential to Logarithmic Form

Alex Cutbill

Express 2⁸ = 256 in its equivalent logarithmic form.


Video Transcript

Express two to the power of eight equals 256 in its equivalent logarithmic form.

You can check that two to the power of eight is indeed 256. This expresses a relationship between the numbers two, eight, and 256, and what we call “exponential form.” There’s another way of writing this relationship, which is called “logarithmic form.” In general, the relationship a to the power of 𝑥 equals 𝑏, which is said to be an exponential form, can be written in logarithmic form as log base a of 𝑏 equals 𝑥.

We can see this in our example: a is two, 𝑥 is eight, and 𝑏 is 256. Writing this in logarithmic form is just a case of substituting the numbers in.

So we write a log, which stands for the logarithm, then the value of a, which is called the base of that logarithm, in our case two, then the value of 𝑏, which in our case is 256. And finally, we say this equals eight. There’s nothing particularly deep going on here; we’re just using different notation to express the same relationship.